The profit optimization problem lies at the heart of markdown pricing and inventory allocation. It represents the prescriptive analytics layer—the point where predictive demand models are translated into actionable decisions that maximize expected profit under uncertainty.
Retailers, especially in e-commerce, face thin margins, short product life cycles, and fixed inventories that cannot be replenished mid-season. Under such conditions, optimizing pricing and allocation jointly—while accounting for uncertain demand parameters—becomes a stochastic programming challenge.
In its most general form, the profit optimization problem seeks to find the optimal price policy $p^$ that maximizes the expected profit (or revenue) under uncertain demand parameters $\Theta$.
Let $f(\theta)$ denote the probability density function of the demand parameters. Then, the expected revenue function is defined as:
About the author
Cyril Noirot
Lead Data Scientist
Freelance data scientist. I design and ship decision systems — forecasting, pricing, marketing measurement, optimization.